The latest round of vote-counting released by the Los Angeles County registrar shows an outsider candidate maintaining his lead over a state senator in a close contest for a runoff spot in the race to replace retiring county Supervisor Michael D. Antonovich.

The outcome of the primary election has been in limbo since June 7. Out of eight candidates, Antonovich’s chief of staff, Kathryn Barger, finished first by a comfortable margin, winning about 30% of the vote. But the second spot remains in question.

Darrell Park, an entrepreneur and former White House Office of Management and Budget staffer, was second in the initial vote count, by a margin of about 400 votes, with state Sen. Bob Huff third. Barger and Huff are Republicans, as is Antonovich; Park is a Democrat.

The county registrar has been counting the outstanding provisional and late vote-by-mail ballots since election day. With the latest count released Friday, Park still held just over 15% of the vote and Huff just under 15%, with Park now ahead by 1,661 votes.